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On the existence of monotone selections

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  • Kukushkin, Nikolai S.

Abstract

For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while each value is chain-complete. (2) The correspondence is ascending while the target is a sublattice of the Cartesian product of a finite number of chains. (3) Both source and target are chains while the correspondence is generated by the maximization of a strongly acyclic interval order with the single crossing property. The theorems give new sufficient conditions for the existence of (epsilon) Nash equilibria.

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File URL: http://mpra.ub.uni-muenchen.de/15845/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14451.

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Date of creation: 03 Apr 2009
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Handle: RePEc:pra:mprapa:14451

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Keywords: Monotone selection; (weakly) ascending correspondence; interval order; single crossing; (epsilon) Nash equilibrium;

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  1. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  2. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
  3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  4. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
  5. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  6. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  7. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
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